#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 16 Maths Textbook Solution.

$\! \! \! \! \! \! \! \! \! x=2\: or\: 4\\y=4\: or\: 2\\z=-6\\w=4$

Given:  $\begin{bmatrix} xy &4 \\ z+6&x+y \end{bmatrix}=\begin{bmatrix} 8 &w \\ 0& 6 \end{bmatrix}$

Here we have to find the value of  $x,y,z,w$

Hint: Here we will use equality of matrices.

Solution:
$\begin{bmatrix} xy &4 \\ z+6&x+y \end{bmatrix}=\begin{bmatrix} 8 &w \\ 0& 6 \end{bmatrix}$

The corresponding entries of equal matrices are equal, So

$xy=8$                                                                                                                                              ….. (i)

$w=4$                                                                                                                                                ….. (ii)

$z+6=0$                                                                                                                                          ….. (iii)

$x+y=6$                                                                                                                                          ….. (iv)

From equation (ii) and (iii) we get

$z=-6$  and $w=4$

From eqn (iv) we have,

$x+y=6\Rightarrow x=6-y$

Substituting the value of $x$  in eqn (i), we get

$\! \! \! \! \! \! \! \! \left ( 6-y \right )y=8\\\Rightarrow y^{2}-6y+8=0\\\Rightarrow \left ( y-2 \right )\left ( y-4 \right )=0\\\Rightarrow y=2 \: or\: 4$

Substituting the value of $y$  in eqn (i), we get

$x=4,2$
Hence value of $x,y,z,w$  are  $4,2;2,4;-6$  and $4$ respectively.

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